Introduction to Classical Mechanics · Problem 7.15
Angular momentum, Part I (Constant L) — Morin
Physics — Mechanics · gravity-kepler-laws
Problem
Closest approach **
A particle with speed v0 and impact parameter b starts far away from a planet of mass M.
((a)) Starting from scratch (that is, without using any of the results from Section 7.4), find the distance of closest approach to the planet.
((b)) Use the results of the hyperbola discussion in Section 7.4.3 to show that the distance of closest approach to the planet is k/(ϵ+1), and then show that this agrees with your answer to part (a).